Hence, the shear tensor and the expansion are trivial on the black hole horizon, the surface gravity is finite there and is equal to
\(g_{{\cal H}}=(4M)^{-1}\)  as it should be.The fact of finiteness of the stress-tesor components near the horizon of static and stationary balck holes even on account of quantum corrections to gravity action was pointed out in [1]}, [2]}, [3]}, [4]}, [5]}.
